Output Tracking of Uncertain Nonminimum Phase Systems by Experience Replay

The precision output tracking problem of multi-input-multi-output (MIMO) uncertain nonlinear nonminimum phase systems is investigated in this paper. The challenge lies in the difficulty in solving the ideal internal dynamics (IID), which is a bounded solution for the uncertain zero dynamics. First, the experience replay technique is applied to identify the uncertain parameters in the zero dynamics. It uses the recorded past data concurrently with current data which can greatly speed up the identification convergence. With the identified parameters, a novel approach called optimal bounded inversion is proposed to obtain the IID by solving a trajectory optimization problem using GPOPS-II. The boundedness of the IID is guaranteed by setting state constraints and the feasibility is achieved by minimizing the initial condition mismatch. Moreover, a piecewise IID updating scheme is adopted to reduce the computational burden. The benchmark nonminimum phase system, a vertical take-off and landing (VTOL) aircraft is used to validate the effectiveness of the proposed method.